Hillary Clinton thinks she’s come up with an ideal counterweight to offset Rudy Giuliani‘s post-9/11 popularity – but actually, she’s only revealed yet again what 9/11 means most to her: more victims for Uncle Sam to take care of.

And that’s precisely the wrong lesson to draw – particularly for someone who appears well on her way to becoming the Democratic Party’s nominee for president next year.

And it couldn’t contrast more sharply with the moral that Giuliani has taken from the attack.

Clinton’s effort to best Giuliani on this score came in a TV ad she unveiled Thursday focusing on health care.

The ad shows images of 9/11 and says Clinton “stood by Ground Zero workers who sacrificed their health after so many sacrificed their lives – and kept standing ’til this administration took action.”

In so doing, New York’s junior senator becomes the first 2008 presidential candidate from either party to use 9/11 footage to hawk a political message.

Not that there’s necessarily anything wrong with that. But who would’ve thought the first 9/11 message from a candidate would be about . . . health care?

Actually, Clinton had already signaled how her presidency would view the most horrific attack on U.S. soil in history.

Last month, for example, she said: “From the first moment that I came to Ground Zero on the day of the evil attacks . . . I knew we were going to have problems . . . That people were going to get sick and people were going to die from what they were exposed to.”

Clinton promised to “rescue the rescuers.” Doing so, she vowed, would “be my highest priority – whether I am your senator or your president. I will stay with this until you get the health care, the treatment and the compensation that you deserve to have.”

Give her points for honesty, anyway.

But now compare that with what Giuliani wrote in a recent essay:

“Full recognition of the first great challenge of the 21st century came with the attacks of Sept. 11, 2001,” he said, “even though Islamist terrorists had begun their assault on world order decades before. Confronted with an act of war on American soil, our old assumptions about conflict between nation-states fell away. Civilization itself, and the international system, had come under attack by a ruthless and radical Islamist enemy.”

The former mayor has spoken often about his leadership of the city in the hours and days after the attack.

In his trip to London last month, he noted how he had looked to Churchill for inspiration on 9/11 itself – forgoing sleep to read about Churchill’s resolve in the face of the German onslaught.

You can bet that on the day of the attacks Giuliani wasn’t thinking about who, down the road, could qualify for new federal health benefits.

With a more than 30-point lead among Democrats, Clinton seems ever more likely to win her party’s nomination. Giuliani’s fate is less clear, though he remains a leader among GOP contenders.

If the two do wind up facing off in the general election, the choice will be stark.

Voters will have no doubt about Clinton’s transmutation of the meaning of 9/11 into a sad story of victimology and enhanced entitlements.

That may work politically, but it’s not likely to do America much good.